Equal angles in Feynman Lecture 26 Figure 26-4 geometry

[Sparky_]

Hello,

Just for fun - I am trying to go through The Feynman’s Lectures: Lecture #26 – Volume 1: The Principle Of Least Time. I am stuck on Figure 26-4 and specifically showing the two angles with the “double arcs” are equal. The angle of reflection BCN’ and XCF.

Maybe I am just that rusty on my geometry – I have going through several pages of scribbles trying to show those two angles are equal with no luck.

Help??

Should a take a picture and attach it to this thread or ?? How can I present the figure?
Thanks

Sparky_

 

[berkeman]

Should a take a picture and attach it to this thread or ?? How can I present the figure?
Thanks

Yes please. Use the "Attach files" link below the Edit window to upload a JPEG or PDF file, or you should be able to do a copy-paste into the Edit window directly, as long as the little icons above the Edit window are not red (click the "[ ]" BB toggle button there to turn the icons black if they are red).

 

[hutchphd]

I am stuck on Figure 26-4 and specifically showing the two angles with the “double arcs” are equal. The angle of reflection BCN’ and XCF

They are not exactly equal, but they are smoothly equal in the limit of small changes in angle. That is all Feynman claims (see egn 26.3 et seq) and all he needs for his least time argument. Its good that you can't prove it!